Section 1

Economics for Pleasure and Profit
Chapter 1

What Is Economics?

Economics is often thought of either as the
answers to a particular set of questions (How do you prevent
unemployment? Why are prices rising? How does the banking system
work? Will the stock market go up?) or as the method by which such
answers are found. Neither description adequately defines economics,
both because there are other ways to answer such questions
(astrology, for example, might give answers to some of the questions
given above, although not necessarily the right answers) and because
economists use economics to answer many questions that are not
usually considered "economic" (What determines how many children
people have? How can crime be controlled? How will governments
act?).

I prefer to define economics as a particular way
of understanding behavior; what are commonly thought of as economic
questions are simply questions for which this way of understanding
behavior has proved particularly useful in the past:

Economics is that way of understanding behavior
that starts from the assumption that people have objectives and tend
to choose the correct way to achieve them.

The second half of the assumption, that people
tend to find the correct way to achieve their objectives, is called
rationality. This term is somewhat deceptive, since it
suggests that the way in which people find the correct way to achieve
their objectives is by rational analysis--analyzing evidence, using
formal logic to deduce conclusions from assumptions, and so forth. No
such assumption about how people find the correct means to achieve
their ends is necessary.

One can imagine a variety of other explanations
for rational behavior. To take a trivial example, most of our
objectives require that we eat occasionally, so as not to die of
hunger (exception--if my objective is to be fertilizer). Whether or
not people have deduced this fact by logical analysis, those who do
not choose to eat are not around to have their behavior analyzed by
economists. More generally, evolution may produce people (and other
animals) who behave rationally without knowing why. The same result
may be produced by a process of trial and error; if you walk to work
every day, you may by experiment find the shortest route even if you
do not know enough geometry to calculate it. Rationality in this
sense does not necessarily require thought. In the final section of
this chapter, I give two examples of things that have no minds and
yet exhibit rationality.

Half of the assumption in my definition of
economics was rationality; the other half was that people have
objectives. In order to do much with economics, one must strengthen
this part of the assumption somewhat by assuming that people have
reasonably simple objectives; with no idea at all about what
people's objectives are, it is impossible to make any prediction
about what people will do. Any behavior, however peculiar, can be
explained by assuming that the behavior itself was the person's
objective. (Why did I stand on my head on the table while holding a
burning $1,000 bill between my toes? I wanted to stand on my
head on the table while holding a burning $1,000 bill between my
toes.)

To take a more plausible example of how a somewhat
complicated objective can lead to apparently irrational behavior,
consider someone who has a choice between two identical products at
different prices. It seems that for almost any objective we can think
of, he would prefer to buy the less expensive item. If his objective
is to help the poor, he can give the money he saves to the poor. If
his objective is to help his children, he can spend the money he
saves on them. If his objective is to live a life of pleasure and
luxury, he can spend the money on Caribbean cruises and
caviar.

But suppose you are taking a date to a movie. You
know you are going to want a candy bar, which costs $1.00 in the
theater and $0.50 in the Seven-Eleven grocery you pass on your way
there. Do you stop at the store and buy a candy bar? Do you want your
date to think you are a tightwad? You buy the candy bar at the
theater, impressing your date (you hope) with the fact that you are
the sort of person who does not have to worry about money.

One could get out of this problem by claiming that
the two candy bars are not really identical; the candy bar at the
theater includes the additional characteristic of impressing your
date. But if you follow this line of argument, no two items are
identical and the statement that you prefer the lower priced of two
identical items has no content. I would prefer to say that the two
items are identical enough for our purposes but that in this
particular case your objective is sufficiently odd so that our
prediction (based on the assumption of reasonably simple objectives)
turns out to be wrong.

WHY ECONOMICS MIGHT
WORK

Economics is based on the assumption that people
have reasonably simple objectives and choose the correct means to
achieve them. Both halves of the assumption are false; people
sometimes have very complicated objectives and they sometimes make
mistakes. Why then is the assumption useful?

Suppose we know someone's objective and also know
that half the time that person correctly figures out how to achieve
it and half the time acts at random. Since there is generally only
one right way of doing things (or perhaps a few) but very many wrong
ways, the "rational" behavior can be predicted but the "irrational"
behavior cannot. If we predict this person's behavior on the
assumption that he is rational, we will be right half the time. If we
assume he is irrational, we will almost never be right, since we
still have to guess which irrational thing he will do. We are
better off assuming he is rational and recognizing that we will
sometimes be wrong. To put the argument more generally, the tendency
to be rational is the consistent (and hence predictable) element in
human behavior. The only alternative to assuming rationality (other
than giving up and concluding that human behavior cannot be
understood and predicted) would be a theory of irrational
behavior--a theory that told us not only that someone would not
always do the rational thing but also which particular irrational
thing he would do. So far as I know, no satisfactory theory of
that sort exists.

There are a number of reasons why the assumption
of rationality may work better than one would at first think. One is
that we are often concerned not with the behavior of a single
individual but with the aggregate effect of the behavior of many
people. Insofar as the irrational part of their behavior is random,
its effects are likely to average out in the aggregate.

Suppose, for example, that the rational thing to
do is to buy more hamburger the lower its price. People actually
decide how much to buy by first making the rational decision then
flipping a coin. If the coin comes up heads, they buy a pound more
than they were planning to; if it comes up tails, they buy a pound
less. The behavior of each individual will be rather unpredictable,
but the total demand for hamburger will be almost exactly the same as
without the coin flipping, since on average about half the coins will
come up heads and half tails.

A second reason why the assumption works better
than one might expect is that we are often dealing not with a random
set of people but with people who have been selected for the
particular role they are playing. Consider the heads of companies. If
you selected people at random for the job, the assumption that they
want to maximize the company's profits and know how to do so would
not be a very plausible one. But people who do not want to maximize
profits, or do not know how to, are unlikely to be chosen for the
job; if they are, they are unlikely to keep it; if they do, their
companies are likely to become increasingly unimportant in the
economy, until eventually the companies go out of business. So the
simple assumption of profit maximization plus rationality turns out
to be a good way to predict how firms will behave.

A similar argument applies to the stock market. We
may reasonably expect that the average investment is made by someone
with an accurate idea of what companies are worth--even though the
average American, and even the average investor, may be poorly
informed about such things. Investors who consistently bet wrong on
the stock market soon have very little to bet with. Investors who
consistently bet right have an increasing amount of their own money
to risk--and often other people's money as well. Hence the
well-informed investors have an influence on the market out of
proportion to their numbers as a fraction of the population. If we
analyze the workings of the market on the assumption that all
investors are well informed, we may come up with fairly accurate
predictions in spite of the inaccuracy of the assumption. In this as
in all other cases, the ultimate test of the method is whether its
predictions turn out to describe reality correctly. Whether something
is an economic question is not something we know in advance. It is
something we discover by trying to use economics to answer
it.

SOME SIMPLE EXAMPLES OF ECONOMIC
THINKING

So far, I have talked of economics in the
abstract; it is now time for some concrete examples. I have chosen
examples involving issues not usually considered economic in order to
show that economics is not a particular set of questions to be
answered but a particular way of answering questions. I will begin
with two very simple examples and then go on to some slightly more
complicated ones.

You are laying out a college campus as a
rectangular pattern of concrete sidewalks with grass between them.
You know that one of the objectives of many people, including many
students, is to get where they are going with as little effort as
possible; you suspect most of them realize that a straight line is
the shortest distance between two points. You would be well advised
to take precautions against students cutting across the lawn.
Possible precautions would be constructing fences or diagonal
walkways, adding tough ground cover, or replacing the grass with
cement and painting it green.

One point to note. It may be that everyone will be
better off if no one cuts across the lawn (assuming the students like
to look at green lawns without brown paths across them). Rationality
is an assumption about individual behavior, not group behavior. The
question of under what circumstances individual rationality does or
does not lead to the best results for the group is one of the most
interesting questions economics investigates. Even if a student is in
favor of green grass, he may correctly argue that his decision to cut
across provides more benefit (time saved) than cost (slight damage to
the grass) to him. The fact that his decision provides
additional costs, but no additional benefits, to other people who
also dislike having the grass damaged is irrelevant unless making
those other people happy happens to be one of his objectives. The
total costs of his action may be greater than the total benefits; but
as long as the costs to him are less than the benefits to him, he
takes the action. This point will be examined at much greater length
in Chapter 18, when we discuss public goods and
externalities.

A second simple example of economic thinking is
Friedman's Law for Finding Men's Washrooms--"Men's rooms are
adjacent, in one of the three dimensions, to ladies' rooms." One of
the builder's objectives is to minimize construction costs; it costs
more to build two small plumbing stacks (the set of pipes needed for
a washroom) than one big one. So it is cheaper to put washrooms close
to each other in order to get them on the same stack. That does not
imply that two men's rooms on the same floor will be next to each
other (although men's rooms on different floors are usually in the
same position, making them adjacent vertically).Putting them next to
each other reduces the cost, but separating them gets them close to
more users. But there is no advantage to having men's and ladies'
rooms far apart, since they are used by different people, so they are
almost always put on the same stack. The law does not hold for
buildings constructed on government contracts at cost plus 10
percent.

As a third example, consider someone making two
decisions--what car to buy and what politician to vote for. In either
case, the person can improve his decision (make it more likely that
he acts in his own interest) by investing time and effort in studying
the alternatives. In the case of the car, his decision determines
with certainty which car he gets. In the case of the politician, his
decision (whom to vote for) changes by one ten-millionth the
probability that the candidate he votes for will win. If the
candidate would be elected without his vote, he is wasting his time;
if the candidate would lose even with his vote, he is also wasting
his time. He will rationally choose to invest much more time in the
decision of which car to buy--the payoff to him is enormously
greater. We expect voting to be characterized by rational
ignorance; it is rational to be ignorant when the information
costs more than it is worth.

This is much less of a problem for a concentrated
interest than for a dispersed one. If you, or your company, receives
almost all of the benefit from some proposed law, you may well be
willing to invest enough resources in supporting that law (and the
politician who wrote it) to have a significant effect on the
probability that the law will pass. If the cost of the law is spread
among many people, no one of them will find it in his interest to
discover what is being done to him and oppose it. Some of the
implications of that will be seen in Chapter 19, where we explore the
economics of politics.

In the course of this example, I have subtly
changed my definition of rationality. Before, it meant making the
right decision about what to do--voting for the right
politician, for example. Now it means making the right decision about
how to decide what to do--collecting information on whom to
vote for only if the information is worth more than the cost of
collecting it. For many purposes, the first definition is sufficient.
The second is necessary where an essential part of the problem is the
cost of getting and using information.

A final, and
interesting, example is the problem of winning a battle. In modern
warfare, many soldiers do not fire their guns in battle, and many of
those who fire do not aim. This is not irrational behavior--on the
contrary. In many situations, the soldier correctly believes that
nothing he can do is very likely to determine who wins the battle; if
he shoots, especially if he takes time to aim, he is more likely to
get shot himself. The general and the soldier have two objectives in
common. Both want their army to win. Both also want the soldier to
survive the battle. But the relative importance of the second
objective is much greater for the soldier than for the general. Hence
the soldier rationally does not do what the general rationally wants
him to do.

Interestingly enough, studies of U.S. soldiers in
World War II revealed that the soldier most likely to shoot was the
member of a squad who was carrying the Browning Automatic Rifle. He
was in a situation analogous to that of the concentrated interest;
since his weapon was much more powerful than an ordinary rifle (an
automatic rifle, like a machine gun, keeps firing as long as you keep
the trigger pulled), his actions were much more likely to determine
who won--and hence whether he got killed--than the actions of an
ordinary rifleman.

The problem is not limited to modern war. The old
form of the problem (which still exists in modern armies) is the
decision whether to stand and fight or to run away. If you all stand,
you will probably win the battle. If everyone else stands and you
run, your side may still win the battle and you are less likely to
get killed (unless your own side notices what you did and shoots you)
than if you fought. If everyone runs, you lose the battle and are
quite likely to be killed--but less likely the sooner you start
running.

One proverbial solution to this problem is to burn
your bridges behind you. You march your army over a bridge, line up
on the far side of the river, and burn the bridge. You then point out
to your soldiers that if your side loses the battle you will all be
killed, so there is no point in running away. Since your troops do
not run and the enemy troops (hopefully) do, you win the battle. Of
course, if you lose the battle, a lot more people get killed than if
you had not burned the bridge.

We all learn in high school history how, during
the Revolutionary War, the foolish British dressed their troops in
bright scarlet uniforms and marched them around in neat geometric
formations, providing easy targets for the heroic Americans. My own
guess is that the British knew what they were doing. It was, after
all, the same British Army that less than 40 years later defeated the
greatest general of the age at Waterloo. I suspect the mistake in the
high school history texts is not realizing that what the British were
worried about was controlling their own troops. Neat geometric
formations make it hard for a soldier to advance to the rear
unobtrusively; bright uniforms make it hard for soldiers to hide
after their army has been defeated, which lowers the benefit of
running away.

The problem of the conflict of interest between
the soldier as an individual and the soldiers as a group is nicely
illustrated by the story of the battle of Clontarf, as given in
Njal Saga. Clontarf was an eleventh century battle between an
Irish army on one side and a mixed Irish-Viking army on the other
side. The Vikings were led by Sigurd, the Jarl of the Orkney Islands.
Sigurd had a battle flag, a raven banner, of which it was said that
as long as the flag flew, his army would always go forward, but
whoever carried the flag would die.

Sigurd's army was advancing; two men had been
killed carrying the banner. The Jarl told a third man to take the
banner; the third man refused. After trying unsuccessfully to find
someone else to do it, Sigurd remarked, "It is fitting the beggar
should bear the bag," cut the banner off the staff, tied it around
his own waist, and led the army forward. He was killed and his army
defeated. The story illustrates nicely the essential conflict of
interest in an army, and the way in which individually rational
behavior can prevent victory. If one or two more men had been willing
to carry the banner, Sigurd's army might have won the battle--but the
banner carriers would not have survived to benefit from the
victory.

And you thought economics was about stocks and
bonds and the unemployment rate.

PUZZLE

You are a hero with a broken sword (Conan,
Boromir, or your favorite Dungeons and Dragons character) being
chased by a troop of bad guys (bandits, orcs, . . .). Fortunately
you are on a horse and they are not. Unfortunately your horse is
tired and they will eventually run you down. Fortunately you have
a bow. Unfortunately you have only ten arrows. Fortunately, being
a hero, you never miss. Unfortunately there are 40 bad guys. The
bad guys are strung out behind you, as shown.

Problem: Use economics to get
away.

Note: You cannot talk to the bad guys. They
are willing to take a substantial chance of being killed in order
to get you--after all, they know you are a hero and are still
coming. They know approximately how many arrows you have.

OPTIONAL SECTION

SOME HARDER EXAMPLES--ECONOMIC
EQUILIBRIA

So far, the examples of economic reasoning have
not involved any real interaction among the rational acts of
different people. We dealt either with a single rational
individual--the architect deciding where in the building to put
washrooms--or with a group of rational individuals all doing more or
less the same thing. Very little in economics is this simple. Before
we start developing the framework of price theory in the next
chapter, you may find it of interest to think through some more
difficult examples of economic reasoning, examples in which the
outcome is an equilibrium produced by the interaction of a number of
rational individuals.

I will use economics to analyze two familiar
situations (supermarket lines and crowded expressways), showing how
economics can produce useful and nonobvious results and how the
argument can be expanded to deal with successively higher levels of
complexity. The logical patterns that appear in these examples
reappear again and again in economic analysis. Once you clearly
understand when and why supermarket lines are all the same length and
lanes in the expressway equally fast, and why and under what
circumstances they are not, you will have added to your mental tool
kit one of the most useful concepts in economics.

Supermarket Lines

You are standing in a supermarket at the far end
of a row of checkout counters with your arms full of groceries. The
line at your end blocks your view of the other lines; you know your
line is long, but you do not know if the others are any shorter.
Should you stagger from line to line looking for the shortest line,
or should you get in the nearest one?

The first and simplest answer is that all the
lines will be about the same length, so you should get into the one
next to you; it is not worth the cost of searching for a shorter one.
Why?

Consider any two adjacent lines in Figure 1-1, say
Lines 4 and 5. Some shoppers will approach the checkout area not from
one end, as you did, but from the aisle that lies between those two
lines. Since those shoppers can easily see both lines, they will go
to whichever one appears shorter. By doing so, they will lengthen
that line and shorten the other; the process continues until both
lines are the same length. The same argument holds for every other
pair of adjacent lines, so all lines will be the same length. It is
not worth it for you to make a costly search for the shortest
line.

There are a number of implicit assumptions in this
argument. When these assumptions are false the argument may break
down. Suppose, for example, that you are at the far end of the row of
checkout counters because that is where the ice cream freezer and the
refrigerator with the cold beer are located. Many other customers
also choose to get these things last and so enter the checkout area
from that end. Even if everyone who comes in between Lines 1 and 2
goes to Line 2, there are not enough such people to make Line 2 as
long as Line 1. If everyone understands the argument of the previous
paragraph and acts accordingly, Line 1 will be longer than Line 2
(and probably much longer than the other lines), and the conclusion
of the argument will be wrong.

Imagine that you program a computer to assign
customers to lines in a way that equalizes the length of the two
lines, as described above, and tell it that 10 people per minute are
entering the checkout area at one end (where they can only see Line
1) and 6 per minute are entering between the two lines. The computer
informs you that of the 6 customers coming in between the two lines,
8 must go to Line 2 and -2 to Line 1. Since 10 customers are going to
Line 1 from the end, the total number going to Line 1 is 10 plus -2,
which equals 8--the number going to Line 2. The computer, having
solved the problem you gave it, sits there with a satisfied
expression on its screen.

You then reprogram it, pointing out that fewer
than zero customers cannot go anywhere. Mathematically speaking, you
are asking the computer to solve the problem subject to the condition
that a certain number (the number of customers coming in between the
two lines and going to one of them) cannot be negative. The computer
replies that in that case, the best it can do is to send all six
customers to Line 2--leaving the lines still unequal.

This sort of result is called a corner
solution because it corresponds to the mathematical situation
where the maximum of a function is not at the top of its graph but
instead at a corner where the graph ends, as shown in Figure 1-2a. In
such a situation, the normal conclusion (in the supermarket case,
that all the lines must be the same length) may no longer hold. The
corresponding result in Figure 1-2a is that the graph is not
horizontal at its maximum--as it would be if the maximum were at an
interior solution, as it is in Figure 1-2b. In
economics--especially mathematical economics--the usual role of
corner solutions is to provide annoying exceptions to general
theorems.

Supermarket, viewed from above. Lines tend
to be equal; Line 1 is a special case because many customers get ice
cream and cold beer last.

Are there other situations in which the
conclusion--that all lines will be the same length--does not hold?
Yes.

So far, I have assumed that for people coming in
between two lines, it is costless to see which line is shorter. This
is not always true. The relevant length, after all, is not in space
but in time; you would rather enter a line of ten customers with only
a few items each than a line of eight customers with full carts.
Estimating which line is shorter requires a certain amount of mental
effort. If the system works so well that all lines are exactly the
same length (in time), then it will never be worth that effort. Hence
no one will make it; hence there will be nothing keeping the lines
the same length. In equilibrium the length of lines must differ by
just enough to repay (on average) the effort of figuring out which
line is shorter. If it differed by more than that, everyone would
look for the shortest line, making all lines the same length
(assuming no corner solution). If it differed by less than that,
nobody would.

It may have occurred to you that I am assuming all
customers have the same ability to estimate how long a line will
take. Suppose a few customers know that the checker on Line 3 is
twice as fast as the others. The experts go to Line 3. Line 3 appears
to be longer than the other lines (to nonexperts, that is; allowing
for the fast checker, the line is actually shorter, in time although
not in length). nonexperts avoid Line 3 until it shrinks back to the
same length as the others. The experts (and some lucky
nonexperts--the ones who are still in Line 3) get out twice as fast
as everyone else.

Word spreads; the number of experts increases. As
long as, with all the experts going through Line 3, Line 3 can still
be as short (in appearance) as the other lines, the increasing number
of experts does not reduce the payoff to being an expert. Every time
one more expert enters the line (making it appear slightly longer
than the others), one more nonexpert decides not to enter
it.

Two maxima--a corner solution (a) and an
interior solution (b). At the interior maximum, the slope of the
curve is zero; at the corner maximum, it need not be.

Eventually the number of experts becomes large
enough to crowd out all the nonexperts from that line. As the number
of experts increases further, Line 3 begins to lengthen. It cannot be
brought back to the same length as the other lines by the defection
of nonexperts (who mistakenly believe that it is longer in waiting
time as well as length) because there are none of them going to it
and the experts know better. Eventually the number of experts becomes
so great that Line 3 is twice as long as the other lines and takes
the same length of time as they do; the gain from being an expert has
now vanished.

To put the same argument in more conventional
economic language, rational behavior (in the sense of "making the
right decision") requires information. If that information is itself
costly, rational behavior consists of acquiring information (paying
information costs) only as long as the return from additional
information is at least as great as the cost of getting it. If
certain minimal information is required to equalize the time-length
of lines, then the time-length of lines must be sufficiently unequal
so that the saving from knowing which line is shorter just pays the
cost of acquiring that information. That principle applies to both
the cost of looking at lines to see which is shortest and the cost of
studying checkers to learn which ones are faster. The initial
argument was given in an approximation in which information was
costless; such an approximation greatly simplifies many economic
arguments but should be used with care.

There is at least one more hidden assumption in
the argument as given. I have assumed that everyone in the grocery
store wants to get out as quickly as possible. Suppose the grocery
store (Westwood Singles Market) is actually the local social center;
people come to stand in long lines gossiping with and about their
friends and trying to make new ones. Since they do not want to get
out as fast as possible, they do not try to go to the shortest line;
so the whole argument breaks down.

Rush Hour Blues

A similar analysis can be applied to lanes on the
freeway. When you are driving on a crowded highway, it always seems
that some other lane is going faster than yours; the obvious strategy
is to switch to the faster lane. If you actually try to follow such a
strategy, however, you discover to your amazement that a few minutes
after you switch lanes, the battered blue pickup that was behind you
in the lane you left is now in front of you.

To understand why it is so difficult to follow a
successful strategy of lane changing, consider that by moving into a
lane you slow it down. If there is a faster lane then people will
move into it, equalizing its speed with that of the other lanes, just
as people moving into a short line lengthen it. So a lane remains
fast only as long as drivers do not realize it is.

Here again, a more sophisticated analysis would
allow for the costs (in frayed nerves and dented fenders) of
continual lane changes. On average, if everyone is rational, there
must be a small gain in speed from changing lanes--if there were not,
nobody would do it and the mechanism described above would not work.
The payoff must equal the cost for the marginal lane
changer--the least well qualified of those following the
lane-changing strategy. If the payoff were less than that, he would
not be a lane changer; if it were more, someone else would. In
principle, if you knew how much a strategy of lane changing cost each
driver (in dents and nerves--less for those with strong nerves and
old cars) and how many lane changers it took to reduce the benefit
from lane changing by any given amount, you could figure out who
would be the marginal lane changer and how much the gain from lane
changing would be. By the end of the course, you should see how to do
this. If you see it now, you are already an economist--whether or not
you have studied economics.

Even More Important Applications to Think
About

Doctors make a lot of money. Doctors also spend
many years as medical students and interns. The two facts are not
unrelated. Different wages in different professions are set by a
process similar to that described above. If one profession is, on
net, more attractive than another (taking account of wages, risks,
costs of learning the profession, and so on), more people go into the
more attractive profession and by so doing drive down the wages. All
professions are in some sense equally attractive--to the marginal
person. In deciding what profession you want to enter, it is not
enough to ask what profession pays the highest wage. Not only are
there other factors, there is also reason to expect that the other
factors will be worst where the wage is best. What you should ask
instead is what profession you are particularly suited for in
comparison to other people making similar choices. This is like
deciding whether to follow a lane-switching strategy by considering
how old your car is compared to others, or deciding whether to look
for a shorter line in the grocery store according to how much you are
carrying.

A similar argument applies to the stock market. It
is often said that if a company is doing very well, you should buy
its stock. But if everyone else knows that the company is doing well,
then the price of its stock already reflects that information. If
buying it were really such a good deal, who would sell? The company
you should buy stock in is one that you know is doing better than
most other investors think it is--even if in some absolute sense it
is not doing very well.

A friend of mine has been investing successfully
for several years by following almost the opposite of the
conventional wisdom. He looks for companies that are doing very badly
and calculates how much their assets would be worth if they went out
of business. Occasionally he finds one whose assets are worth more
than its stock. He buys stock in such companies, figuring that if
they do well their stock will go up and if they do badly they will go
out of business, sell off their assets--and the stock will again go
up.

If all of this is obvious to you the first time
you read it (or even the second), then in your choice of careers you
should give serious consideration to becoming an
economist.

NEGATIVE FEEDBACK

Several of the situations described in this
chapter involved a principle called negative feedback. A familiar
example of negative feedback is driving a car. If the car is going to
the right of where you want it, you turn the wheel a little to the
left; if it is going to the left of where you want, you turn it a
little to the right. This is called feedback because an error in the
direction you are going "feeds back" into the mechanism that controls
your direction (through you to the steering wheel). It is negative
feedback because an error in one direction (right) causes a
correction in the other direction (left). An example of positive
feedback is the shriek when the amplifier attached to a microphone is
turned up too high. A small noise comes into the mike, is amplified
by the amplifier, comes out of the speaker, and feeds back into the
mike. If the amplification is high enough, the noise becomes louder
each time around, eventually overloading the system.

In the supermarket line example, the lines are
kept at about the same length by negative feedback: If a line gets
too long compared to other lines people stop going to it, which makes
it get shorter. Similarly, when a lane on the expressway speeds up,
cars move into it, slowing it down. In each case, what we are mostly
interested in are not the details of the feedback process but rather
the nature of the stable equilibrium--the situation such that
deviations from it cause correcting feedback.

RATIONALITY WITHOUT MIND

In defending the assumption of rationality, I
pointed out that it is not the same as the assumption that people
reason logically. Logical reasoning is not the only, or even the most
common, way of getting a correct answer. I will demonstrate this with
two extreme examples--cases in which we observe rationality in
something that cannot reason, since it has no mind to reason with. In
the first case, I will show how a mindless object--a collection of
matchboxes filled with marbles--can learn to play a game rationally.
In the second, I will show how the rational pursuit of objectives by
genes--mindless chains of atoms inside your cells--explains a
striking fact about the real world, something so fundamental that it
never occurs to most of us to find it surprising.

Computers that Learn

Suppose you want to build a computer to play some
simple game, such as tic-tac-toe. One way is to build in the correct
move for every situation. Another, and in some ways more interesting,
approach is to let the computer teach itself how to play. Such a
learning computer starts out moving randomly. Each time a game ends,
the computer is told whether it won or lost and adjusts its strategy
accordingly, lowering the probability of moves that led to losses and
increasing the probability of moves that led to wins. After enough
games, the computer may become a fairly good player.

The computer does not think. Its "mind" is simply
a device that identifies the present situation of the game, chooses a
move by some random mechanism, and later adjusts the probabilities
according to whether it won or lost. A simple version consists of a
bunch of matchboxes filled with black and white marbles, laid out on
a diagram of the game. Moves are chosen by picking a marble at
random, with the color of the marble determining the move. The mix of
marbles in each matchbox is adjusted at the end of the game to make
moves that led to a win more likely and moves that led to a loss less
likely.

A matchbox computer, or its more sophisticated
electronic descendants, does not think, yet it is rational. Its
objective is to win the game and, after it has played long enough to
"learn" how to win, it tends to choose the correct way of achieving
that objective. We can understand and predict its behavior in the
same way that we understand and predict the behavior of humans.
"Rationality" is simply the ability to get the right answer; it may
be the result of many things other than rational thinking.

Economics and
Evolution

There is a close historical connection between
economics and evolution. Both of the discoverers of the theory of
evolution (Darwin and Wallace) said they got the idea from Thomas
Malthus, an economist who was also one of the originators of the
so-called Ricardian Theory of Rent (named after David Ricardo, who
used it but did not invent it), one of the basic building blocks of
modern economics.

There is also a close similarity in the logical
structure of the two fields. The economist expects people to choose
correctly how to achieve their objectives but is not very much
concerned with the psychological question of how they do so. The
evolutionary biologist expects genes--the fundamental units of
heredity that control the construction of our bodies--to construct
animals whose structure and behavior are such as to maximize their
reproductive success (roughly speaking, the number of their
descendants), since the animals that presently exist are descended
from those that were reproductively successful in the past and carry
the genes that made them successful. The biologist need not be
concerned very much with the detailed biochemical mechanisms by which
the genes control the organism. Many of the same patterns appear in
both economics and evolutionary biology; the conflict between
individual interest and group interest that I mentioned earlier
reappears in the conflict between the interest of the gene and the
interest of the species.

A nice example is Sir R.A. Fisher's explanation of
observed sex ratios. In many species, including ours, male and female
offspring are produced in roughly equal numbers. There is no obvious
reason why this is in the interest of the species; one male suffices
to fertilize many females. Yet the sex ratio remains about 1:1, even
in some species in which only a small fraction of the males succeed
in reproducing. Why?

Fisher's answer is as follows. Imagine that two
thirds of offspring are female, as shown in Figure 1-3. Consider
three generations. Since each individual in the third generation has
both a father and a mother, if there are twice as many females as
males in the second generation, the average male must have twice as
many children as the average female. This means that an individual in
the first generation who produces a son will, on average, have twice
as many grandchildren as one who produces a daughter. Individual A on
Figure 1-3, for example, has six children, while Individual B only
has three. A's parents got twice as great a return in grandchildren
for producing A as B's parents did for producing B.

If there are more females than males in the
population, couples who produce sons have more descendants, on
average, than those who produce daughters. Since couples who produce
sons have more descendants, more of the population is descended from
them and has their genes--including the gene for having sons. Genes
for producing male offspring increase in the population.

The initial situation, in which two thirds of the
population in each generation was female, is unstable. As long as
more than half of the children are female, genes for having male
children spread faster than genes for having female children; so the
percentage of female children falls. Similarly, if more than half the
children were male, genes for having female children would have the
advantage and spread. Either way, the situation must swing back
towards an even sex ratio.

In making this argument, I implicitly assumed
equal cost for producing male and female offspring. In a species with
substantial sexual dimorphism (male and female babies of different
size), the argument implies that the total weight of female offspring
(weight per offspring times number of offspring) will be about the
same as that for male offspring. One could add further complications
by considering differences in the costs of raising male and female
offspring to maturity. Yet even the simple argument is strikingly
successful in explaining one of the observed regularities of the
world around us by the "rational" behavior of microscopic entities.
Genes cannot think--yet in this case and many others, they behave as
if they had carefully calculated how to maximize their own survival
in future generations.

Three generations of a population with a
male:female ration of 1:2. Members of the first generation who
have a son produce twice as many grandchildren as those who have a
daughter, so genes for having sons increase in the population,
swinging the sex ratio back toward 1:1.

PROBLEMS

1. In defending the rationality assumption, I
argued that while people sometimes make mistakes, their correct
decisions are predictable and their mistakes are not. Can you think
of any alternative approaches to understanding human behavior that
claim to predict the mistakes? Discuss.

2. Give examples (other than buying candy for your
date--the example discussed in the text) of apparently irrational
behavior that consists of choosing the correct means to achieve an
odd or complicated end.

3. In this chapter and throughout the book I treat
individual preferences as givens--I neither judge whether people have
the "right" preferences nor consider the possibility that something
might change individual preferences.

a. Do you think some preferences are better than
others? Give examples. Discuss.

b. Describe activites that you believe can only be
understood as attempts to change people's preferences. How would you
try to analyze such activities in economic terms?

4. Friedman's Law for Finding Men's Washrooms
could be described as fossilized rationality--whether the architect
lives or dies, his rationality remains set in concrete in the
building he designed.

a. Can you think of other examples?
Discuss.

b. Can you describe any cases where instead of
deducing the shape of something from the rationality of its maker, we
deduce the rationality of its maker from its shape?
Discuss.

5. What devices (other than those discussed in the
text) are used by generals, ancient and modern, to prevent soldiers
from concluding that it is in their interest to run away, not aim, or
in some other way act against the interest of the army of which they
are a part?

6. The problem I have discussed exists not only in
your army but in the enemy's army as well. Discuss ways in which a
general might take advantage of that fact, giving real-world examples
if possible.

7. In a recent conversation with one of our deans,
I commented that I was rather absent-minded--I had missed two or
three faculty meetings that year--and wished I could get him to make
a point of reminding me when I was supposed to be somewhere. He
replied that he had already solved that problem, so far as the
(luncheon) meetings he was responsible for. He made sure I would not
forget them by always arranging to have a scrumptious chocolate
dessert.

a. Is this an economic solution to the problem of
getting me to remember things? Discuss.

b. In what sense does or does not the success of
this method indicate that I "choose" to forget to go to meetings?
Discuss.

8. This chapter discusses situations where
rational behavior by each individual leads to results that are
undesirable for all. Give an example of such a situation in your own
experience; it should not be one discussed in the chapter.

9. Many voters are rationally ignorant of the
names of their congressmen. List some things you are rationally
ignorant of. Explain why your ignorance is rational. Extra credit if
they are things that many people would say you ought to
know.

The following problems refer to the optional
section:

10. The analyses of supermarket lines, freeway
lanes, and the stock market all had the same form. In each case, the
argument could be summarized as "The outcome has a particular pattern
because if it did not, it would be in the interest of people to
change their behavior in a way that would push the outcome closer to
fitting the pattern." Such a situation is called a stable
equilibrium. Can you think of any examples not discussed in the
text?

11. Analyze express lanes in supermarkets. Is the
express lane always faster? If not, when is it and when is it
not?

12. In the supermarket example, I started by
assuming that you had your arms full of groceries. Why? How does that
assumption simplify the argument?

13. The friend whose investment strategy I
described is a very talented accountant. When I met him, he was in
his early twenties and was making a good income teaching accounting
to people who wanted to pass the CPA exam. Does this have anything to
do with his investment strategy?

14. Is there any reason why my accountant friend
should prefer that this book, or at least this chapter, not be
published?

15. Give some examples of negative and positive
feedback in your own experience.

16. Certain professions are very attractive to
their members and very badly paid. Consider the stereotype of the
starving artist--or a friend of mine who is working part-time as a
store clerk while trying to make a career as a professional lutenist.
Is the association between job attractiveness and low pay accidental,
or is there a logical connection? Discuss.

17. You have been collecting data on the behavior
of a particular stock over many years. You notice that every Friday
the 13th, the stock drops substantially, only to come back up over
the next few weeks; your conclusion is that superstitious
stockholders sell their stock in anticipation of bad luck. What can
you do to make use of this information? What effect does your action
have? Suppose more people notice the behavior of the stock and react
accordingly; what is the effect?

18. Generalize your answer to the previous
question to cover other situations where a stock price changes in a
predictable way. What does this suggest about schemes to make money
by charting stock movements and using the result to predict when the
market will go up?

19. Suppose that in Floritania the total cost of
bringing up a son is three times the cost of bringing up a daughter,
since Floritanians do not believe in educating women. Floritanians
simply love grandchildren; every couple wants to have as many as
possible. Due to a combination of modern science and ancient
witchcraft, Floritanian parents can control the gender of their
offspring. What is the male/female ratio in the Floritanian
population? Explain.

20. The principal foods of the Floritanians are
green eggs and ham. It costs exactly twice as much to produce a pound
of green eggs as a pound of ham. The more green eggs that are
produced, the lower the price they sell for, and similarly with
ham.

a. You are producing both green eggs and ham.
Green eggs sell for $3/pound; so does ham. How could you increase
your revenue without changing your production cost?

b. What will be the result on the prices of green
eggs and ham?

c. If everyone acts rationally, what can you say
about the eventual prices of green eggs and ham in
Floritania?

FOR FURTHER READING

For a good introduction to the economics of genes
I recommend Richard Dawkins's The Selfish Gene (New York:
Oxford University Press, 1976).

A more extensive discussion of the economics of
warfare can be found in my essay, "The Economics of War," in J.E.
Pournelle (ed.), Blood and Iron (New York: Tom Doherty
Associates, 1984).

For a very different application of economic
analysis to warfare, I recommend Donald W. Engels's Alexander the
Great and the Logistics of the Macedonian Army (Berkeley:
University of California Press, 1978). The author analyzes
Alexander's campaigns while omitting all of the battles. His central
interest is in the problem of preventing a large army from dying of
hunger or thirst and the way in which that problem determined much of
Alexander's strategy. Consider, as a very simple example, the fact
that you cannot draw water from a well, or 5 wells, or 20 wells, fast
enough to keep an army of 100,000 people from dying of
thirst.

The relationship between individual rationality
and group behavior is analyzed in Thomas Schelling's Micromotives
and Macrobehavior (New York: W.W. Norton and Co.,
1978).